Question 67: Properties of Matter

Question

A small spherical ball of radius $$r$$, falling through a viscous medium of negligible density has terminal velocity '$$v$$'. Another ball of the same mass but of radius $$2 r$$, falling through the same viscous medium will have terminal velocity:

Accepted Answer

Since density is negligible hence Buoyancy force will be negligible
At terminal velocity.
$$\mathrm{Mg} =6 \pi \eta \mathrm{rv}$$
$$\mathrm{V}  \propto \frac{1}{\mathrm{r}} \quad$$ (as mass is constant)
Now, $$\frac{\mathrm{v}}{\mathrm{v}^{\prime}}=\frac{\mathrm{r}^{\prime}}{\mathrm{r}}$$
$$r^{\prime}=2 \mathrm{r}$$
So, $$v^{\prime}=\frac{v}{2}$$

Answer

$$4 \mathrm{v}$$

Answer

$$2 \mathrm{~V}$$

Answer

$$\frac{v}{4}$$

Answer

$$\frac{\mathrm{v}}{2}$$

Properties of Matter

A small spherical ball of radius $r, falling through a viscous medium of negligible density has terminal velocity 'v'. Another ball of the same mass but of radius 2 r$, falling through the same viscous medium will have terminal velocity:

Choose the correct answer: